板材成形无网格法模拟中的关键技术处理

Treatment of key technologies involved in meshless simulation of sheet metal forming

针对有限元法费时的网格划分/网格重划问题,提出采用无网格法模拟板材成形.采用约束型再生核子法描述板材成形力学方程,仅用一层节点离散板材,同时对形函数进行改造,所得动可容形函数具有插值性,避免了大变形所导致的不稳定形函数及频繁构造形函数,提出了稀疏矩阵数据结构加快接触搜索方法.基于上述措施建立了板材冲压成形无网格数值模拟程序,实现了板材冲压成形无网格模拟.研究表明,该方法可大幅减小模拟所需节点数,有效提高计算效率,并消除剪切自锁及精确施加本征边界条件,说明该方法是可行可靠的.

In this paper,the constrained reproducing kernel formulation was adopted to describe the equations governing the sheet metal forming under cartesian coordinate by one lay of nodes,and the revised meshless shape function called admissible shape function was used to impose essential boundary conditions.Furthermore,an approach was presented to overcome the difficulties such as instability of shape function and frequent update of shape function,which resulted from large deformation.Based on these,a meshless simulation of sheet metal forming was carried out and the results showed that the new method can accurately impose the essential boundary condition and overcome the problem of shear locking,and it needs only small number of nodes,so that the computational efficiency can be increased greatly.